BREAK ’EM UP! Joel Sherman says putting the Yankees and Red Sox in different divisions would be one way to create more competition in the American League. Photo: Charles Wenzelberg/New York Post

Baseball does not have a competitive-balance problem. It might have a Yankees problem or a Yankees-Red Sox problem. But mainly it has a public relations problem.

There is no salary cap and the Yankees have a payroll that dwarfs all others. That combination — more than anything — creates the perception that the sport lacks competitive balance. But repeating that over and over does not make it fact. Here is a fact: Eight different teams have won the World Series in the last decade or one more than has won the Super Bowl in the sainted, share-every-dollar NFL.

How can the Royals ever compete with the Yankees? Sounds great. It is repeated all the time. Just, it is ridiculous. The Royals’ biggest problem isn’t the Yankees; it is the people running the Royals. How about Kansas City produce a better record than the Twins one of these years before we worry if it can compete with the Yankees?

The same goes for the Pirates, Nationals, etc. The only teams that have a legitimate gripe about the monster that is the Yankees — and the junior monster that is the Red Sox — are the Rays, Orioles and Blue Jays. They are in the same division.

That brings us to realignment, which became a hot-button issue again in the last week. That is because my friend Tom Verducci of Sports Illustrated reported that a radical plan was discussed by the 14-member “special committee for on-field matters.” That group, consisting mainly of managers and general managers, was assembled by Bud Selig to advise the commissioner on ways to improve all areas of the game. One idea that gained traction within the group was “floating” realignment, which would allow clubs to shift divisions annually based on, among other things, what a team thought its chances at contention were.

So, for example, if a club believed it was a non-contender it might consider jumping to the AL East as a way to partially escape an expected dismal record by benefitting at the gate from 18 lucrative home dates against the Yankees and Red Sox.

A person with ties to the advisory committee said that powerful people with the commissioner’s ear championed this proposal. Nevertheless, a friend of Selig said that plan has “no shot.” In the past, Selig has favored significant realignment to better honor geography and payroll similarity, but met massive resistance from ownerships unwilling to relocate divisions and/or leagues. There are many impediments to the proposal anyway, including that teams need their schedule for the following year by September to plot — among other things — ticket-selling strategy. Which team would know what division it would want to be in for the following year by September?

But the biggest impediment to this proposal should be common sense. This is proposing killing a mosquito with a Howitzer. Let’s return to the original premise, which is that — at worst — the sport has a Yankees-Red Sox problem. How do we know that? Consider that the Phillies are the Vegas favorites to win the pennant again (I actually like the Rockies if anyone cares). If Philadelphia does win, it would mark a third straight NL title. Yet no one is talking about the NL having a lack of competitive balance.

So why disrupt five divisions? If there is a Yankees-Red Sox problem, then let’s address that. I would implement all three of the following ideas, but any one by itself would help:

1. Put the Yankees or Red Sox in the AL Central

I know it sounds like blasphemy to break up the Rivalry. But the Rivalry is a bit of a sham. It has not been red-hot every year for nine decades. In the late-1990s, the Yankees’ biggest rival was the Orioles. There was a time when the Mets’ main rivals were the Cubs or Cardinals, and the world did not end when both were shifted out of the NL East. Eventually the Mets built rivalries with the Braves and Phillies. Rivalries will bloom from current competition even more than history.

The reality is: If the Yankees and Red Sox are away from each other, their chances of making the playoffs both probably rise (because both could finish first in a division), but what also rises is the chances of the teams that finish second in those divisions also making the playoffs. Right now the Rays might be the third-best team in the majors, finish third in the AL East and not make the playoffs. If teams in the AL East only had to beat out the Yankees OR the Red Sox — not both — there would be greater hope within the division.

2. Eliminate the unbalanced schedule

Eighteen games against each division opponent are too much. Yes, clubs such as Baltimore and Toronto love all those home dates against Boston and New York for attendance reasons. But the chances to compete diminish when 22 percent of your schedule (36 games) is exclusively against the Yankees and Red Sox. There is no reason why the number cannot be dropped to 12-14 games.

3. Add an additional wild card team

Of all the ideas, this one seems to have the most traction, with one AL executive saying he has heard no objections to the concept recently and pegging it at “no less than an 80 percent chance” that it will be incorporated by 2012.

If you read this space (thanks), you know I have championed this idea for nearly a decade: Have the two wild-card winners in each league play a best-of-three over three consecutive days beginning the day after the regular season concludes. The fringe benefits include that you would intensify division races because the winners get a few days off after the season to rest and line up their pitching. You would never again see a team that has clinched the wild card but still could win the division not play all out to win the division.

In addition, you also honor the team with the best record in each league by having it play the wild-card series winner, meaning a well-rested team would get to use its No. 1 starter against a team with no rest that might have to use its No. 4 starter in a series opener.

In five of the last seven years, the Yankees and Red Sox have made up 50 percent of the AL’s four playoff teams. So let’s at least drop that to 40 percent by adding an extra wild card. Would there be some scheduling issues? Yes. But the commissioner already is committed to removing so many extraneous off-days in the postseason plus the season could start a few days earlier and the schedule could include two or three day-night doubleheaders and, voila, you have created necessary days for a wild-card series.

An extra wild card — like splitting up the Yankees and Red Sox or undoing the unbalanced schedule — would mean more teams in contention in July and August. Which not only would elevate hope but eliminate a lot of those salary-dumping trades that also generally favor teams such as the Yankees and Red Sox, and give the illusion of competitive imbalance.